1. Field of the Invention
This invention relates to mathematical teaching aids, and more particularly, to mathematical teaching aids incorporating a balance beam for illustrating and verifying mathematical operations involving integral and non-integral numbers.
2. Description of the Prior Art
Mathematical teaching aids incorporating a balance beam typically includes a horizontally oriented balance arm which has attachment points for weights located at predetermined spaced intervals. Weights are normally attached to the balance arm by hooks, pans or pegs. The weights which are used in conjunction with the balance beam are typically all of equal mass or of integral multiples of a mass unit (e.g. 1, 5, 10, 25 mass units per weight). Because of the quantizement of the weights into integral values and due to the uniform spacing between each of the attachment points for the weights along the length of the balance arm, these prior art mathematical teaching aids are useable only with equations which include integers. For instance, a balance beam of the design illustrated in U.S. Pat. No. 3,486,244 (the Horn patent) can be used to illustrate that the sum of the integers 4 + 3 + 2 = 9. An instructor must prepare equations which students can then solve with the assistance of the Horn balance beam. The Horn apparatus is unable to solve an equation in which 1.21 is added to 3.86 to produce the resulting sum of 4.07. Furthermore, it would be possible for a student to attempt to solve a problem which would exceed the limits of the Horn apparatus. This situation would occur if a student attempted to add 4 + 3 + 5 which would require an answer of 12, but numbers of this magnitude do not appear as possible alternatives on the Horn balance beam.
Clearly, a device such as that illustrated in the Horn patent is useful, but extremely limited in that each of the weights is identical to the others and these weights can only be attached to the balance beam arm at predetermined equal intervals.
Although the Horn apparatus can be used to perform addition, subtraction, multiplication and division, it can only demonstrate these mathematical operations. If a student wishes to verify the results of a mathematical operation which he has performed himself, it might very well be impossible for the Horn apparatus to accomplish that task. Verification would be impossible with the Horn device if the answer exceeded a certain predetermined magnitude or if the answer failed to yield an integral number. While the Horn mathematical teaching aid is useful, it can be readily seen that it has serious shortcomings.
Another mathematical teaching aid is disclosed by Stults in U.S. Pat. No. 3,567,221. The Stults device is substantially similar to that disclosed by Horn, but further includes weights which are magnetically coupled together and which can be subdivided into either smaller or larger mass units. Again, however, the Stults device provides attachment points for these weights only at predetermined intervals upon the balance arm and therefore suffers from the same shortcomings as the Horn device.
Heinichen in U.S. Pat. No. 3,212,202 discloses an additional embodiment of an arithmetic teaching aid. While somewhat different in appearance and structure from the Horn device, the Heinichen device also requires a plurality of equal weight tokens which are positionable in uniformly spaced recesses along the length of the balance beam. While this device can perform the functions of addition, subtraction, multiplication and division, the device can only operate with integral numbers to produce integral results.
Other prior art mathematical teaching aids are illustrated in the following U.S. Pat. Nos. 3,339,291 (Ruchlis), 1,415,278 (Tod). Each of these devices is basically similar in nature and operation to the Horn device and suffers from the same shortcomings.
Other balance beam inventions which are less related to the present invention are disclosed in the following patents: U.S. Pat. Nos. 3,224,521 (Czanderna), 1,404,426 (Becker), 849,418 (Nickerson), 3,188,089 (Odell), 2,955,811 (Jonas), 591,202 (Witzel), and 2,672,754 (Kent).